The Loudspeaker Radiation Space - Tip 4

An enclosed dynamic loudspeaker drive unit has theoretically ideal working conditions only if its frontal radiation space is either a full or a half space (i.e. spherical or hemi-spherical radiation). In practice the radiation angle decreases as the frequency increases first because of the finite size of the front baffle of the loudspeaker cabinet and secondly because of the size of the drive unit itself. When a loudspeaker is then placed near a wall, the wall presents an extension of the baffle of the loudspeaker at low frequencies, its frequency response will be modified, and we experience a bass boost

Because the space has a strong effect on the radiation, it is important to understand the initial conditions. The radiation space is typically characterized by a rough estimate of the solid angle (part of a sphere) into which the loudspeaker is radiating (see below). As the loudspeaker- subwoofer is driven, it creates a certain volume flow, which naturally spreads into all directions. When the space seen by the loudspeaker is limited and at the same time the total power is kept identical, the energy density (intensity) in the limited radiation space increases. Hence, reducing the radiation space increases Sound Pressure Level (SPL). Every halving of the radiation space doubles the SPL.

tip4 fig1

Spherical loading
Free-space (4pi)

Free-standing

Hemispherical loading
Half-space (2pi)

Flush-mounting

2 walls loading
Quarter-space (pi)

Floor / wall

3 walls loading
1/8th-space (pi/2)

Floor / 2 walls



Concerning the usual placement of a loudspeaker/subwoofer, we notice that:

  • Against one solid boundary, which is large compared to the wavelength, the radiation space is 2pi, and the theoretical amplitude gain is up to +6 dB at low frequencies. This applies typically to flush mounting.
  • A subwoofer is typically placed on the floor and against a wall, hence we get two boundaries, and the radiation is now into the solid angle of pi, and the amplitude gain is up to +12 dB.
  • If a loudspeaker or a subwoofer is located in a corner, on the floor, the radiation space is again halved (pi/2) and the amplitude gain is then up to +18 dB.
It is essential to note that in this context words like ”large”, ”close”, etc. always refer to the wavelength. ”Large” compared for example to 10 m (34 Hz) is different from ”large” compared to 3.4 m (100 Hz) or 3.4 cm (10 kHz). This means that when a loudspeaker is placed ”far” from boundaries at, say, 150 Hz, it probably is very ”close” at 30 Hz.

The radiation space depends on frequency and therefore it is important to be able to correct the response of the loudspeaker/subwoofer so that the final in-room frequency response stays as flat as possible. To do so, all Genelec monitors have versatile room response controls to take care of these changes in radiation spaces.